Ways to animate edge loops sliding along a torus knot
Sadly you can not do this directly, however you can achieve the same result fairly easily. Begin by selecting one longitudinal edge loop, and pressing P > By Selection. Now (in object mode) delete the old mesh. Next select the new edge loop mesh, and press Alt+C > Curve from Mesh/Text.



Now you can create a cylinder, add an array and curve modifier, and you have the desired result. You may need to scale and adjust your cylinder mesh slightly to fine tune it.



Simply animate the mesh's position (on the Z axis) to animate the edge loop sliding effect, and add your wireframe modifier to complete the effect.



And this is what the final result will look like:



The array modifier has been disabled to show the animation more clearly.